 if not zero, is the eigenstate of momentum operator \({\hat{P}}\)  with eigen quantum number \({\bf q}\) . Thus, exciton states, in contrast to single electron states, possess a natural quantum number, namely, the 2D momentum whose existence is the consequence of the translational invariance. We study CSFE at \(\nu \!=\!2\) , hence in our case \(a\!=\!(0,\downarrow )\)  and \(b\!=\!(1,\uparrow )\) . The \({\cal Q}_{{\bf q}}^{\dag }|0\rangle \)  state (we omit the `\(ab\) ' index, besides, note that \({\cal Q}_{{\bf q}}|0\rangle \!\equiv \!0\) ) represents an eigen state of our quantum Hall system yielding, in accordance with the solution of the many-electron Schrödinger equation,[1]}, [2]} the CSFE energy to the first order in terms of parameter \(r_s\)  with the \(q\) -dispersion part:
